Transition to parametric wave patterns in a vertically oscillated granular layer

Francisco Melo, Paul Umbanhowar, Harry L. Swinney
1994 Physical Review Letters  
The standing wave patterns formed on the surface of a vertically oscillated fluid enclosed by a container have long been a subject of fascination, and are known as Faraday waves. In circular containers, stable, radially symmetrical Faraday wave-patterns are resonant phenomena, and occur at the vibrational modes where whole numbers of waves fit exactly onto the surface of the fluid sample. These phenomena make excellent systems for the study of pattern formation and complex nonlinear dynamics.
more » ... nlinear dynamics. We provide a systematic exploration of variables that affect Faraday wave pattern formation on water in vertical-walled circular containers including amplitude, frequency, volume (or depth), temperature, and atmospheric pressure. In addition, we developed a novel method for the quantification of the time taken for patterns to reach full expression following the onset of excitation. The excitation frequency and diameter of the container were the variables that most strongly affected pattern morphology. Amplitude affected the degree to which Faraday wave patterns were expressed but did not affect pattern morphology. Volume (depth) and temperature did not affect overall pattern morphology but in some cases altered the time taken for patterns to form. We discuss our findings in light of René Thom's catas-trophe theory, and the framework of attractors and basins of attraction. We suggest that Faraday wave phenomena represent a convenient and tractable analogue model system for the study of morphogenesis and vibrational modal phenomena in dynamical systems in general, examples of which abound in physical and biological systems.
doi:10.1103/physrevlett.72.172 pmid:10055594 fatcat:tkds44xrmndv3fhmolq54mfwwq